ivj.wJL.Lw.Ln
Substituting this value of G in the torque equation we have T doo 0 _,.. 0
I-rr = - 2FDCOS-
dt 2
h
FIRST APPROXIMATION. When 0 and <£ are small the following relations give close enough approximations.
m 1 0
T = img, cos- = 1, 2
D
JDO ==: 6</>j sin <j!> == 0== ~r 0.
Making these substitutions in the torque equation we get
du _ __ m^D2
which is the equation of simple harmonic motion. Therefore
mg
is the period of the motion.
SECOND APPROXIMATION. From Fig. 143 we have
FIG. 143.
and ea'= Zsin</>= 2Dsin- -
-2
Therefore and
2D . 0 sin 0 = sin ~
I 2i
T =
sin2 ^
* The line ea' is considered as an arc of each of two circles with centers at g and c.